Ariana invested $400 in an account paying an interest rate of 3.8% compounded
monthly. Assuming no deposits or withdrawals are made, how much money, to the
nearest ten dollars, would be in the account after 11 years?

The measures of the indicated angles are 35 °, 238.73° & 18.40 ° respectively.

What are the trigonometric identities?

All trigonometric identities are based on the six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent are the values. All of these trigonometric ratios are defined using the sides of a right triangle, such as an adjacent side, opposite side, and hypotenuse side.

Let's consider,

x = opposite side of an angle of the triangle.

y = adjustant side of an angle of the triangle.

z = hypotenuse of the triangle.

θ = angle of the triangle.

i) In the first diagram

We have,

y = 49

z = 60

[tex]cos\theta = \frac{y}{z}[/tex]

θ = cos⁻¹(0.816)

θ = 35 °

ii) In the second diagram

We have,

y = 41

x = 10

θ = ?

[tex]tan\theta = \frac{x}{y}[/tex]

θ = tan⁻¹(0.2439)

θ = 238.73°

i) In the third diagram

y = 53

x = 17

θ = ?

[tex]tan\theta = \frac{x}{y}[/tex]

θ = tan⁻¹(3.11)

θ = 18.40 °

Hence, the measures of the indicated angles are 35 °, 238.73° & 18.40 ° respectively.

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Answer:

30 lb

Step-by-step explanation:

75% of trash is recyclable.

40 lb trash.

75% of 40 lb = = 40/100 × 75 lb = 0.40 × 75 lb = 30 lb

Answer: 30 lb

Answer:

$594

Step-by-step explanation:

450x1.32=$594

450+32%=$594

Answer: The answer would be 8ft

Step-by-step explanation:

The formula for the perimeter of a rectangle in terms of the width w is w=(P-2l)/2.

Given that, the formula for the perimeter of a rectangle is P=2(l+w).

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Here, the perimeter is  P=2(l+w)

⇒ P=2l+2w

⇒ P-2l=2w

⇒ w=(P-2l)/2

Hence, the formula for the perimeter of a rectangle in terms of the width w is w=(P-2l)/2.

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Answer: 25% of 12 is 3

Step-by-step explanation:

Since there 25% is 1/4 of 100%, you'd need to divide.

There are 12 pints of berries.

If 1/2 of 25% is 6 since [tex]2 \sqrt{12}=6[/tex], you can say that the percentage would be 2/4.

Now, divide 12 by 4: [tex]4\sqrt{12}=3[/tex]

3 in this case would be the 1/4 and the 1/4 is substituting 25%

So there are 3 pints of blueberries.

The population in the next 20 years would be 2653 people. The result is obtained by the equation of estimating the future population.

The future population can be estimated by the following equation:

P = P₀ × (1 + i)ⁿ

Where

If the recent population is 1000 people and the growth rate is 5% per year, what would the population be in the next 20 years?

The population in the next 20 years would be

P = P₀ × (1 + i)ⁿ

P = 1000 × (1 + 0.05)²⁰

P = 1000 × (1.05)²⁰

P = 1000 × 2.6533

P = 2653 people

Hence, the population in the next 20 years would be 2653 people.

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According to the solving the co-ordinate mid-point D is (-4,0).

A point on a line which bisects the same line is a mid point. It divides the line in two equal halves.

The mid-point is equidistant from both the ends of the given line.

Middle point formula in coordinate geometry

M={(x1+x2)/2,(y1+y2)/2}

We need to find the coordinates of mid-point D of line AB, where

A is (-6x,4y)

B is (-2x,-4y)

By using Mid-point formula for coordinate D, we get

   x=-6+(-2)/2

⇒ x=-6-2/2

⇒x=-8/2

⇒x=-4

And y coordinate

y=4+(-4)/2

⇒y=4-4/2

⇒y=0/2

⇒y=0

The coordinates of mid-point D of line AB is (-4,0)

Hence, D is (-4,0)

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Using mathematical operations, we know that 15 cartons can hold 1,305 wooden blocks.

So, a number of blocks 15 cartons can hold:

We know that,

Now, calculate as follows:

Therefore, using mathematical operations, we know that 15 cartons can hold 1,305 wooden blocks.

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Answer:

18%,1/8,18%, 8/20 0.8

Step-by-step explanation:

0.8 8/100 18/100 1/8 8/20

0.8 , 0.08 0.18 0.12 0.4

0.08 0.12 0.18 0.4 0.8

Answer:

8%, 1/8, 18%, 8/20

Step-by-step explanation:

Lets make all of these into decimals (its easier that way).
8% = 0.08
18% = 0.18
1/8 = 0.125

8/20 = 0.4

Now, put them into least to greatest! :)

Answer:

total is discarding 7 tables for you the Fall Festival by placing the same number of paper skeletons and bats on each table all together he used 84 scouters and 84 bats how many paper shapes went on each table

Answer:

(5x5) + (5x2)

Step-by-step explanation:

is that helpful i dont really get what youre asking

Answer:

1+2*3*5+4

Step-by-step explanation:

The equation that represents the line  that is perpendicular to the graph of 4x + 3y = 9 and passes through (-2,3) is

[tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]

Let us revise some rules

1.   The product of the slopes of the perpendicular line is -1, that means if the slope of one line is m, then the slope of the other is [tex]\frac{-1}{m}[/tex]

2.  The slope of a line whose equation is ax + by = c is [tex]m = \frac{-a}{b}[/tex], where a is the coefficient of x and b is the coefficient of y

The equation of the given line is 4x + 3y = 9

[tex]m = \frac{-a}{b}[/tex]

whereas a is the coefficient of x and b is the coefficient of y

Therefore the coefficient of x = 4 and the coefficient of y = 3

a = 4 and b = 3

[tex]m = \frac{-a}{b}[/tex]

The slope of the perpendicular line to the given line is [tex]\frac{-1}{m}[/tex]

That means reciprocal the fraction and change its sign

The slope of the perpendicular line = [tex]\frac{3}{4}[/tex]

The form of the equation is y = mx + b

- Substitute m by [tex]\frac{3}{4}[/tex]

y = [tex]\frac{3}{4}[/tex] x + b

To find b substitute x and y in the equation by the coordinates

of a point on the line

The perpendicular line passes through point (-2 , 3)

x = -2 and y = 3

3 = [tex]\frac{3}{4}[/tex](-2) + b

3 = [tex]\frac{-3}{2}[/tex]+ b

Add to both sides

[tex]\frac{9}{2}[/tex] = b

y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]

The equation that represents the line  that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]

Hence the answer is perpendicular to graph of 4x+3y=9 and passes through (-2,3) is [tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]

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Answer:

------------------------

Answer:

32.3x + 136.85y

Step-by-step explanation:

Let's take it as,

→ z = 100%

Forming the equation,

→ z + 15% = 38x + 161y

Now the value of z will be,

→ z + 15% = 38x + 161y

→ z = 38x + 161y - (1 - (15/100))

→ z = (38x + 161y) × (1 - 0.15)

→ z = (38x + 161y) × (0.85)

→ [ z = 32.3x + 136.85y ]

Hence, the answer is above.

Answer:

4.47 seconds.

Step-by-step explanation:

Given function:

[tex]h(t)=-10t^2+200[/tex]

where:

The rock will hit the ground when h(t) = 0.  

Therefore, set the function to zero and solve for t:

[tex]\begin{aligned}h(t)&=0\\\implies -10t^2+200&=0\\10t^2&=200\\t^2&=20\\t&=\pm\sqrt{20}\\t&=-4.47, 4.47\;\; \sf (2\;d.p.)\end{aligned}[/tex]

As time is positive, t = 4.47 s only.

If a tram moved downward 35 meter in 7 seconds at a constant rate, then the change in the tram's elevation for each second is 5 meter

The total distance that tram moved downwards = 35 meters

Total time taken = 7 seconds

Here we have to use the unitary method

The change in the tram's elevation for each second = The total distance that tram moved downwards / Total time taken

Substitute the values in the equation

The change in the tram's elevation for each second = 35 /7

Divide the terms

= 5 meters

Hence, if a tram moved downward 35 meter in 7 seconds at a constant rate, then the change in the tram's elevation for each second is 5 meter

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Answer:

[tex] \huge{ \bold{f(g(x)) = 4x + 4}} \\ \\ \huge{ \bold{g(f(x)) = 4x - 5}}[/tex]

Step-by-step explanation:

f(x) = 4x-8

g(x)=x+3

In order to find f(g(x)) you substitute g(x) into f(x) that's where ever you find x in f(x) you replace it with g(x) and solve

We have

[tex]f(g(x)) = 4(x + 3) - 8 \\ = 4x + 12 - 8 \\ = 4x + 4[/tex]

In order to find g(f(x)) you substitute f(x) into g(x) that's where ever you find x in g(x) you replace it with f(x) and solve

We have

[tex]g(f(x)) = (4x -8) + 3 \\ = 4x - 8 + 3 \\ = 4x - 5[/tex]

Hope this helps you

As their measure of angles are not the same with respect to the positive x-axis they are not parallel.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know two lines are parallel if their slope is equal.

Given are two lines m and n.

For line m, slope(m) is m/2 = (5x + 3)° where x = 14.

Slope(m) is, m/2 = (5·14 + 3)°.

m/2 = 73°.

m = 146°.

For line n, slope(m) is, m/3 = (8x - 5)° where x = 14.

m/3 = 107°.

m = 321°.

As their measure of an angle is not the same with respect to the positive x-axis these two lines are not parallel.

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option (a) and (C).

The height of the parallelogram is 2 units and 2/3 units.

The sides of parallelogram are 6 units and 18 units .

Area of parallelogram (A) =12 square units.

Base of parallelogram (B) = 6 units.

formula used:

A = B*H

12 = 6*H

H = 12/6

H = 2 units.

if, base of parallelogram (B) = 18 units

A = B*H

12= 18*H

H = 12/18

H = 2/3 units.

the height of parallelogram are 2 and 2/3 units.

#123

For more information:

The parallelogram has a height of 2/3 units.

Given that,

A parallelogram has a surface area of 12 square units. The parallelogram has a side that is 18 units long. There are 6 units on the other side.

For a parallelogram to find the height;

Let,

Area of the parallelogram = Base * Height

12 = 18 * H

H = 12/18

H = 2/3

Therefore, the height of the parallelogram is 2/3 units.

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The length of  CF is 51 inches.

Complete question:

( In triangle ABC in which AD,BE and CF are the medians ),

In △ABC, ​ GF=17 in. ​ What is the length of CF¯¯¯¯¯? Enter your answer in the box.

What is the median in a triangle?

A line segment that joins a vertex to the mid-point of the side that is opposite to that vertex

The centroid G divides each median into the ratio 2:1, so GF is 1/3 of CF. That is, ...

CF = 3(GF) = 3(17 in)

CF = 51 in

So, the length of  CF is 51 inches.

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The value of x=5 if given quadrilateral is parallelogram.

What is parallelogram?

A parallelogram is a flat shape with four straight, connected sides so that opposite sides are congruent and parallel. This means a parallelogram is a plane figure, a closed shape, and a quadrilateral.

We know, the opposite sides of parallelogram are equal

therefore, 5x-8 = 2x+7

5x -2x = 7+8

3x = 15

x =5

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Step-by-step explanation:

false.

QR and ES are line segments.

a ratio between them is about their lengths, not about their position.

so, no, the given ratio has nothing to do with the coordinate itself.

The correct statement is 'the distribution of sample means approaches a normal curve as sample size(n) increases to infinity'

In this question, we have been given a statement 'the distribution of sample means approaches a normal curve as _________  increases to infinity'

We need to complete the statement.

The Central Limit Theorem tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.

This means, the distribution of sample means approaches a normal curve as the sample size i.e., n increases to infinity.

Therefore, the correct statement is 'the distribution of sample means approaches a normal curve as sample size(n) increases to infinity'

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The average of 1 to 9 Integers is 5 because average is computed by adding a set of numbers and then dividing by the total number of those numbers.

By dividing the total number of values by the total number of numbers, the average can be computed. A mean is the mathematical average of a set of two or more data items. Common names for average include mean and mathematical mean. The term "mean" simply represents the average of the sample.

The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the amount of units in the list. The term "mean" in statistics also refers to the average of a particular set of numerical data.

To calculate average = 1+2+3+4+5+6+7+8+9/9

=45/9= 5

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Answer:

Step-by-step explanation:

find the gradient of given equation:

3y+4x=12

3y= -4x+12

y= -4/3x+4

gradient= -4/3

perpendicular gradient:

m1xm2=-1

-4/3m2=-1

-4m2=-3

m2= 3/4

find y-intercept by inputting coordinates in y=mx+c

5=3/4(3)+c

5=9/4+c

5-9/4=c

c= - 11/4

equation:

y=3/4x-11/4

Answer: £4.26

Step-by-step explanation:

i think it is this:

the oranges cost £1.42 per kg and you have 1.5 kg of oranges so do £1.42 x 3=£4.26

Both areas are equal, 4 cm²

Answer:

Area of triangle = 4 cm²

Area of square = 4 cm²

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

From inspection of the given diagram:

Substitute the values into the formula to find the area of the triangle:

[tex]\begin{aligned}\implies A&=\dfrac{1}{2} \times 2 \times 4\\A&=1 \times 4\\A&=4\;\sf cm^2\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]

From inspection of the given diagram:

Substitute the value into the formula to find the area of the square:

[tex]\begin{aligned}\implies A&=2^2\\A&=2 \times 2\\A&=4\;\sf cm^2\end{aligned}[/tex]

The area of the triangle is 4 cm², and the area of the square is 4 cm², thus proving that the triangle and the square have the same area.